Comptes Rendus
Research article - Geometry and Topology
Coxeter-type quotients of surface braid groups
Renato Diniz1; Oscar Ocampo2; Paulo Cesar Cerqueira dos Santos Júnior3
1Universidade Federal do Recôncavo da Bahia – CFP, Av. Nestor de Melo Pita, 535, CEP: 45300.000, Amargosa, BA, Brazil
2Universidade Federal da Bahia, Departamento de Matemática – IME, Av. Milton Santos S/N, CEP: 40170-110, Salvador, BA, Brazil
3Universidade Estadual do Sudoeste da Bahia, Departamento de Ciências Exatas e Tecnológicas – DCET, Estrada do Bem Querer S/N, CEP: 45031-900, Vitória da Conquista, BA, Brazil
Comptes Rendus. Mathématique, Volume 364 (2026), pp. 27-36

Let $M$ be a closed surface, $q\ge 2$ and $n\ge 2$. In this paper, we analyze the Coxeter-type quotient group $B_n(M)(q)$ of the surface braid group $B_{n}(M)$ by the normal closure of the element $\sigma _1^q$, where $\sigma _1$ is the standard Artin generator of the braid group $B_n$. Also, we study the Coxeter-type quotient groups obtained by taking the quotient of $B_n(M)$ by the commutator subgroup of the respective pure braid group $\bigl [{P_n(M),P_n(M)}\bigr ]$ and adding the relation $\sigma _1^q=1$, when $M$ is a closed orientable surface or the disk.

Soit $M$ une surface fermée, $q\ge 2$ et $n\ge 2$. Dans cet article, nous étudions le groupe quotient de type Coxeter $B_n(M)(q)$ du groupe de tresses sur la surface $B_n(M)$, défini comme le quotient par la clôture normale de l’élément $\sigma _1^q$, où $\sigma _1$ désigne le générateur d’Artin standard du groupe de tresses $B_n$. Nous étudions également les groupes quotients de type Coxeter obtenus en quotientant $B_n(M)$ par le sous-groupe dérivé du groupe de tresses pures correspondant $\bigl [{P_n(M),P_n(M)}\bigr ]$ et en ajoutant la relation $\sigma _1^q=1$, lorsque $M$ est une surface orientable fermée ou le disque.

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DOI: 10.5802/crmath.813
Classification: 20F36, 20F05
Keywords: Artin braid group, surface braid group, finite group
Mots-clés : Groupe de tresses d’Artin, groupe de tresses sur une surface, groupe fini

Renato Diniz  1 ; Oscar Ocampo  2 ; Paulo Cesar Cerqueira dos Santos Júnior  3

1 Universidade Federal do Recôncavo da Bahia – CFP, Av. Nestor de Melo Pita, 535, CEP: 45300.000, Amargosa, BA, Brazil
2 Universidade Federal da Bahia, Departamento de Matemática – IME, Av. Milton Santos S/N, CEP: 40170-110, Salvador, BA, Brazil
3 Universidade Estadual do Sudoeste da Bahia, Departamento de Ciências Exatas e Tecnológicas – DCET, Estrada do Bem Querer S/N, CEP: 45031-900, Vitória da Conquista, BA, Brazil
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     title = {Coxeter-type quotients of surface braid groups},
     journal = {Comptes Rendus. Math\'ematique},
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Renato Diniz; Oscar Ocampo; Paulo Cesar Cerqueira dos Santos Júnior. Coxeter-type quotients of surface braid groups. Comptes Rendus. Mathématique, Volume 364 (2026), pp. 27-36. doi: 10.5802/crmath.813

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